Answer:
[tex] \frac{0.75x - 3}{x - 1} [/tex]
Step-by-step explanation:
Equation of a rational function is
[tex] \frac{p(x}{q(x)} [/tex]
where q(x) isn't zero.
There is a vertical asymptote at
[tex]x = 1[/tex]
So this mean that our denomiator must have a zero that occur at x=1.
That zero is
[tex]x - 1[/tex]
So our denomiator is
[tex] \frac{p(x)}{x - 1} [/tex]
Since our horinzontal asymptote is a non zero value, the numerator must be a linear equation as well.
So our rational function is
[tex] \frac{ax + b}{x - 1} [/tex]
We know the graph pass through (0,3)
So if we apply that logic,
[tex] \frac{a(0) + b}{0 - 1} = 3[/tex]
[tex] \frac{b}{ - 1} = 3[/tex]
[tex]b = - 3[/tex]
And it passes through (4,0)
[tex] \frac{a(4) + b}{3} = 0[/tex]
[tex]4a + b = 0[/tex]
[tex]4a + ( - 3) = 0[/tex]
[tex]4a = 3[/tex]
[tex]a = \frac{3}{4} [/tex]
So our rational equation is
[tex] \frac{0.75x - 3}{x - 1} [/tex]
